The problem refers to a given circuit, but the circuit diagram is not included in the prompt. Without the actual circuit connections, sources, and resistor arrangement, the voltage across the $10\,\Omega$ resistor cannot be determined uniquely.

What is missing

To compute the voltage across the $10\,\Omega$ resistor, we need the circuit diagram showing:

1. How the $10\,\Omega$ resistor is connected,
2. The values and locations of other resistors,
3. The battery/source values and polarities,
4. Any special elements such as current sources, switches, etc.

Why the answer cannot be derived

The voltage across a resistor depends on the current through it or the node potentials across it: $V = IR$ So unless the circuit is known, neither $I$ nor the node voltages can be found.

Comparison with stored answer

The stored correct answer is given as $70$, but since the circuit image is absent, I cannot independently verify that value from first principles.

Please provide the circuit diagram, and I can solve it step-by-step and verify whether the answer is indeed $70$.